# Find the slope of the tangent to the curve y = 3x^{4} - 4x at x = 4

**Solution:**

For a curve y = f(x) containing the point (x_{1},y_{1}) the equation of the tangent line to the curve at (x_{1},y_{1}) is given by

y − y_{1} = f′(x_{1}) (x − x_{1})

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

The given curve is

y = 3x^{4} - 4x at x = 4.

Then,

the slope of the tangent to the given curve at x = 4 is given by,

dy/dx]_{x = 4} = d/dx (3x^{4} - 4x)]_{x = 4}

= 12x^{3} - 4]_{x = 4}

= 12 (4)3 - 4

= 12 (64) - 4

= 764

Therefore, the slope of the tangent is 764

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 1

## Find the slope of the tangent to the curve y = 3x^{4} - 4x at x = 4

**Summary:**

The slope of the tangent to the curve y = 3x^{4} - 4x at x = 4 is 764. The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line

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